Frugivory networks exhibit a set of properties characterized by a number of network theory-derived metrics. Their structures often form deterministic patterns that can be explained by the functional roles of interacting species. Although we know lots about how these networks are organized when ecosystems are in a complete, functional condition, we know much less about how incomplete and simplified networks (such as those found in urban and periurban parks) are organized, which features are maintained, which ones are not, and why. In this paper, we examine the properties of a network between frugivorous birds and plants in a small Neotropical periurban park. We found a frugivory network composed of 29 species of birds and 23 of plants. The main roles in this network are played by four species of generalist birds (three resident, one migratory: Myiozetetes similis, Turdus grayi, Chlorospingus flavopectus, and Dumetella carolinensis) and three species of plants (one exotic, two early successional: Phoenix canariensis, Phoradendron sp., and Witheringia stramoniifolia). When compared to reference data from other locations in the Neotropics, species richness is low, one important network-level metric is maintained (modularity) whereas another one is not (nestedness). Nestedness, a metric associated with network specialists, is a feature this network lacks. Species-level metrics such as degree, species strength, and module roles, are not maintained. Our work supports modularity as the most pervasive network-level metric of altered habitats. From a successional point of view, our results suggest that properties revealed by species-level indices may be developed at a later time, lagging the acquisition of structural elements. © 2020 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.